1. Counting irreducible polynomials over finite fields
- Creator:
- Wang, Qichun and Kan, Haibin
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- finite fields, distribution of irreducible polynomials, and residue
- Language:
- English
- Description:
- In this paper we generalize the method used to prove the Prime Number Theorem to deal with finite fields, and prove the following theorem: \[ \pi (x)= \frac q{q - 1}\frac x{{\log _q x}}+ \frac q{(q - 1)^2}\frac x{{\log _q^2 x}}+O\Bigl (\frac {x}{{\log _q^3 x}}\Bigr ),\quad x=q^n\rightarrow \infty \] where $\pi (x)$ denotes the number of monic irreducible polynomials in $F_q [t]$ with norm $ \le x$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public